On the fine regularity of the singular set in the nonlinear obstacle problem

We revisit and sharpen the results from our previous work, where we investigated the regularity of the singular set of the free boundary in the nonlinear obstacle problem. As in the work of Figalli-Serra on the classical obstacle problem, we show that each stratum can be further decomposed into a `good part and an `anomalous part, where the former is covered by $C^{1,1-}$ manifolds, and the latter is of lower dimension.